Lecture Notes on Diffraction, Grating, Resolving Power - College physics | PHYS 102, Study notes of Physics

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Diffraction, Gratings,

Resolving Power

• Textbook sections 25.5-

Physics 102: Lecture 21

Recall

• Interference

(at least 2 coherent waves)

• Constructive (full wavelength difference)– Destructive

(½ wavelength difference)

• Light

(1 source, but different paths)

• Thin Films– Double/multiple slit– Diffraction/single slit

d

Path length difference 1-

Multiple Slits

(Diffraction Grating – N slits with spacing d)

θ

θ

L

= d sin

θ

d

Path length difference 1-3 = 2d sin

θ

d

1 2

3

Path length difference 1-4 = 3d sin

θ =λ

=2λ

=3λ

4

Constructive interference for all paths when

N slits with spacing d

Constructive Interference Maxima are at:

sin

m

λ d

• screenVERY faraway

θ

Diffraction Grating

Same as for Young’s

Double Slit!

For many slits, maxima are still at

sin

m

λ d

Region between maxima gets suppressed moreand more as no. of slits increases – bright fringesbecome narrower and brighter.

10 slits (N=10)

d sin

θ

intensity

λ

2λ

0

2 slits (N=2)

d sin

θ

intensity

λ

2λ

0

Multiple Slit Interference

(Diffraction Grating)

Peak location

depends onwavelength!

Constructive interference:

dsin

m

d

nm

in NaCl

For

λ

=.017nm

X-ray

d

1

st

maximum will be at 10

0

X-Ray Diffraction

Crystal solid such

as sodium

θ

dsin

θ

W

w^2

sin

θ

θ

θ

θ

W

2

1 1

′

Rays 2 and 2

′

also start W/2 apart and have

the same path length difference.

2

2

′

1

st

minimum

at:

When

rays 1 and 1

′

interfere destructively.

w^2

sin

θ =

λ 2

Under this condition, every ray originating in top half ofslit interferes destructively with the corresponding rayoriginating in bottom half.

Single Slit Diffraction

w

Rays 2 and 2

′

also start w/4 apart and have

the same path length difference.

2

nd

minimum at:

Under this condition, every ray originating in top quarter ofslit interferes destructively with the corresponding rayoriginating in second quarter.

Single Slit Diffraction

4 w

θ

1 1

′

)

sin(

4 w

θ

2

2

′

When

rays 1 and 1

′

will interfere destructively.

2

)

sin(

4 w

λ

θ

=

Preflights 21.4, 21.

A laser is shone at a screen through a very small hole. Ifyou make the hole even smaller, the spot on the screenwill get:

(1) Larger

(2) Smaller

Which drawing correctly depicts the pattern of light onthe screen?

(1)

(2)

(3)

(4)

Maxima and minima will be a series of bright anddark rings on screen

Central

maximum

1

st

diffraction

minimum

θ

Diameter D

light

Diffraction from Circular Aperture

First diffraction minimum is at:

These objects are

just resolved

Two objects are just resolved when the maximum ofone is at the minimum of the other.

Physics 102: Lecture 21, Slide

Resolving Power

To see two objects distinctly, need

objects

min

θ

min

θ

objects

Improve resolution by increasing

θ

objects

or decreasing

θ

min

θ

objects

is angle between

objects and aperture:

tan

θ

objects

≈

d/y

sin

θ

min

≈ θ

min

= 1.

λ

/D

θ

min

is minimum angular separation

that aperture can resolve:

D

d

y

sin

min

min

λ D

ACT: Resolving Power

How does the maximum resolving power of your eyechange when the brightness of the room is decreased.1) Increases

2. Constant

3. Decreases

Recap.

• Interference:

Coherent waves

• Full wavelength difference = Constructive– ½ wavelength difference = Destructive

• Multiple Slits

• Constructive d sin(

) = m

m=1,2,3…)

• Destructive

d sin(

) = (m + 1/2)

2 slit only

• More slits = brighter max, darker mins

• Huygens’ Principle:

Each point on wave front acts as

coherent source and can interfere.

• Single Slit:

• Destructive:

w sin(

) = m

m=1,2,3…)

• Resolution:

Max from 1 at Min from 2

opposite!